Short-crested waves interaction with a concentric porous cylinder system with partially porous outer cylinder

In this paper, based on the linear wave theory, the interaction of short-crested waves with a concentric dual cylindrical system with a partially porous outer cylinder is studied by using the scaled boundary finite element method (SBFEM), which is a novel semi-analytical method with the advantages of combining the finite element method (FEM) with the boundary element method (BEM). The whole solution domain is divided into one unbounded sub-domain and one bounded sub-domain by the exterior cylinder. By weakening the governing differential equation in the circumferential direction, the SBFEM equations for both domains can be solved analytically in the radial direction. Only the boundary on the circumference of the exterior porous cylinder is discretized with curved surface finite elements. Meanwhile, by introducing a variable porous-effect parameter G, non-homogeneous materials caused by the complex configuration of the exterior cylinder are modeled without additional efforts. Comparisons clearly demonstrate the excellent accuracy and computational efficiency associated with the present SBFEM. The effects of the wide range wave parameters and the structure configuration are examined. This parametric study will help determine the various hydrodynamic effects of the concentric porous cylindrical structure.     

A coupled numerical model for simulation of wave breaking and hydraulic performances of a composite seawall

A numerical model is developed by combining a porous flow model and a two-phase flow model to simulate wave transformation in porous structure and hydraulic performances of a composite type low-crest seawall. The structure consists of a wide submerged reef, a porous terrace at the top and an impermeable rear wall. The porous flow model is based on the extended Navier-Stokes equations for wave motion in porous media and k−ε turbulence equations. The two-phase flow model combines the water domain with the air zone of finite thickness above water surface. A unique solution domain is established by satisfying kinematic boundary condition at the interface of air and water. The free surface advection of water wave is modeled by the volume of fluid method with newly developed fluid advection algorithm. Comparison of computed and measured wave properties shows reasonably good agreement. The influence of terrace width and structure porosity is investigated based on numerical results. It is concluded that there exist optimum value of terrace width and porosity that can maximize hydraulic performances. The velocity distributions inside and in front of the structure are also investigated.     

Numerical modeling of nonlinear water waves over heterogeneous porous beds

The transformation of nonlinear water waves over porous beds is studied by applying a numerical model based on Chen's [2006. Fully nonlinear Boussinesq-type equations for waves and currents over porous beds. Journal of Engineering Mechanics, 132:2, 220–230] Boussinesq-type equations for highly nonlinear waves on permeable beds. The numerical model uses a high-order time-marching solution and fourth-order finite-difference schemes for discretization of first-order spatial derivatives to obtain a computational accuracy consistent with the model equations. By forcing the wave celerity and spatial porous-damping rate of the linearized model to match the exact linear theory for horizontal porous bed over a prescribed range of relative depths, the values of the model parameters are optimally determined. Numerical simulations of the damped wave propagation over finite-thickness porous layer demonstrate the accuracy of both the numerical model and governing equations, which have been shown by prior theoretical analyses to be accurate for both nominal and thick porous layers. These simulations also elucidate on the significance of the higher-order porous-damping terms and the influence of the hydraulic parameters. Application of the model to the simulation of the wave field around a laboratory-scale submerged porous mound provides a measure of its capability, as well as useful insight into the scaling of the porous-resistance coefficients. For application to heterogeneous porous beds, the assumption of weak spatial variation of the porous resistance is examined using truncated forms of the governing equations. The results indicate that the complete set of Boussinesq-type equations is applicable to porous beds of nonhomogeneous makeup.     

A coupled numerical model of wave interaction with porous medium

A new coupling model of wave interaction with porous medium is established in which the wave field solver is based on the two dimensional Reynolds Averaged Navier-Stokes (RANS) equations with a kε closure. Incident waves, which could be linear waves, cnoidal waves or solitary waves, are produced by a piston-type wave maker in the computational domain and the free surface is traced through the Piecewise Linear Interface Construction-Volume of Fluid (PLIC-VOF) method. Nonlinear Forchheimer equations are adopted to calculate the flow field within the porous media. By introducing a velocity–pressure correction equation, the wave field and the porous flow field are highly and efficiently coupled. The two fields are solved simultaneously and no boundary condition is needed at the interface of the internal porous flow and the external wave. The newly developed numerical model is used to simulate wave interaction with porous seabed and the numerical results agree well with the experimental data. The additional numerical tests are also conducted to study the effects of seabed thickness, porosity and permeability coefficient on wave damping and the pore water pressure responses.     

A highly wave dissipation offshore breakwater

The aim of this paper is to develop an offshore breakwater, for which coefficients of both the wave reflection and transmission have low values. The breakwater is suggested to compose of n layers of porous materials with different porosities. A complex eigen function method is used in the theoretical analysis. Continuities of both mass flux and fluid pressure are assumed at interfaces between every two adjoining porous materials and at the interface between end materials and water region. Following a series of mathematical processes, the coefficients of the wave transmission and reflection along with the wave energy loss are calculated. The porosity of materials is varied in computations; and results are compared among structures composing of different layers of porous materials. A single layer offshore breakwater is shown to reduce simultaneously the coefficients of transmission and reflection only when the structure is very wide in the direction of wave propagation, and the structure material has a high porosity. A multilayer breakwater, however, can function well in reducing both coefficients at a much narrower width; structure having more layers can be more effective at narrower width. Finally, several experiments are conducted; theoretical computations and experimental results agree well.     

Influence of viscosity on one-dimensional thermal consolidation of marine clay

ABSTRACT

The elastic mechanical response of porous materials under a heat source has many applications in civil engineering and has received considerable attention in the geotechnical literature. In this paper, a Kelvin viscoelastic model is combined with the thermohydromechanical governing equations for marine clay and solved using a numerical inversion of the inverse Laplace transform in the time domain. After validation against existing analytical solutions, numerical parametric studies are conducted to investigate the influence of viscosity on temperature, excess pore pressure, and displacement. It is shown that viscosity has little influence on temperature, a modest influence on displacements, and a quite significant influence on excess pore pressure.     

Dynamic response of a large-diameter pile with variable section in layered saturated soil considering construction disturbance effect

ABSTRACT

An analytical solution is developed in this paper to investigate the vertical time-harmonic response of a large-diameter variable-section pile, and it considers the radial inhomogeneity of the surrounding soil caused by construction disturbance. First, the saturated soil surrounding the pile is described by Biot’s poroelastic theory and a series of infinitesimally thin independent layers along the shaft of the pile, and the pile is represented by a variable-section Rayleigh–Love rod. Then, the dynamic equilibrium equations of the soil and pile are solved to obtain an analytical solution for the impedance function at the pile top using the complex stiffness transfer method and impedance function transfer method. Finally, the proposed solution is compared with previous solutions to verify its reliability, and a parameter study is conducted to provide insights into the sensitivity of the vertical dynamic impedance of the pile and velocity response in low-strain integrity testing on defective piles.     

A theory for waves interacting with porous structures with multiple regions

This study presents an analytical solution for the problem of waves passing a submerged porous structure, using a multi-region method in the solution scheme considering the characteristics of geometry and composing materials of the porous structure. Using the flux and pressure conditions on horizontal boundaries and interfaces, the orthogonal property of wave motion within the porous layers through water depth is derived, and applied in the solution process. The flux and pressure conditions on vertical boundaries and interfaces are integrated to give a set of linear matrix equations, through which the unknown coefficients are solved. Comparisons of the present method with previous studies are preceded in verification, which suggests the validity and practicability of the present study, with a further expectation of extending our work to build a mild-slope equation over multiple-layer porous medium in the future.     

Hydromechanical behavior of radially multilayered cylinders under time-varying loads

ABSTRACT

Geotechnical strata are often treated as horizontally homogeneous for hydromechanical analysis due to the vertical deposition of geological layers; however, such a treatment becomes no longer valid when vertical drilling or construction causes the localized disturbance of subsurface, which would result in radial heterogeneity of geomaterials. This paper presents a poroelastic solution for the saturated multilayered cylinder where multilayer is used to represent radial heterogeneity. After the application of Laplace transform, the governing equations in cylindrical coordinates are derived to obtain the stiffness matrix between stresses, displacements, and pore water pressure. The global matrix is assembled by the boundary conditions and the compatibility of interfaces between adjacent layers. Under time-dependent horizontal compression loads, a parametric study is performed for a cylinder comprised of two layers with distinct properties, and the results show that the load frequency and radial heterogeneity play a significant role in hydromechanical behavior of geomaterials: (1) the time-varying loading can induce a negative pore pressure, and the influence of cyclic loading with a high frequency is limited near the outer surface; (2) the radial heterogeneity due to permeability and compressibility affects the development of pore pressure.     

Boundary element analysis of liquid sloshing characteristics in axisymmetric tanks with various porous baffles

This paper aims to investigate the effects of the porous baffles on the suppression of sloshing for the tanks with axisymmetric geometries under lateral excitation. Based on the assumptions of inviscid, irrotational, incompressible liquid and small amplitude sloshing, an axisymmetric boundary element method (BEM) for 3D Laplace equation is derived by using the Green's theorem together with the weighted residual method. And a zoning method is employed to model fluid domain in the tanks with complex porous baffles. Meanwhile, the porous baffles are treated motioning together with the tanks, and the velocity across the porous baffle is assumed to be linearly proportional to the pressure gradient between each side of the porous baffle. And the mechanism of suppressing the sloshing response is mainly the energy dissipation of the fluid passing through the porous baffle. Moreover, the linear free surface boundary conditions are also used to solve the governing equations. Compared with other numerical methods, the most prominent advantage of the BEM in solving axisymmetric potential problem is that only the boundaries of half the cross-section instead of the entire problem domain should be discretized, which can cut down large amount of memory and time costs. The present method is verified by comparing the numerical results with the existing literatures, and excellent agreements are obtained. Meanwhile, the proposed models are applied to investigate the effects of the porous baffles on sloshing response in circular cylindrical, annular cylindrical and conical tanks. The effects of the porous baffle length, porous-effect parameter, installation angle and baffle height on the sloshing force, natural frequency and surface elevation are studied. Additionally, some typical sloshing pressure distributions, velocity potential contours and velocity fields are plotted. The results show that swirls at the tips of the baffles can be observed in many cases, and the top-mounted porous baffle makes more significant suppression effects on sloshing response than that of bottom-mounted porous baffle, while increasing the number of ring porous baffles can achieve better restraint effects on sloshing response. And increasing the baffle length of the horizontal wall-mounted ring porous baffle can significantly decrease the sloshing frequencies, as well as the first non-dimensional natural frequency decreases with decrease in porous-effect parameter of the coaxial porous baffle. In addition, remarkable effects on sloshing can be obtained when reasonable designed by selecting the optimal porous-effect parameter, installation angle and baffle height. And this paper can be a useful guide for the seismic design and analysis of many actual liquid storage tanks (such as the Advanced Passive PWR, large water cooling tower, etc.).     

Numerical simulation of the nonlinear wave-induced dynamic response of anisotropic poro-elastoplastic seabed

Abstract

In this paper, a 2D poro-elastoplastic model for wave-induced dynamic response in an anisotropic seabed is derived analytically. The seabed is treated as a porous medium and characterized by Biot’s consolidation equations. The soil plasticity and wave non-linearity are included in the model and both the pore fluid and the soil skeleton are assumed to be compressible. The nonlinear ocean waves are respectively considered as progressive and standing waves. The previous experimental data is used to validate the proposed model. Numerical results demonstrate that the influence of nonlinear wave components should not be ignored without committing substantial error. A significant difference between progressive and standing waves is also observed for the development of residual pore pressure, as well as the distribution of liquefied zone. A detailed parametric investigation reveals that the nonlinear wave-induced seabed response is also affected significantly by cross-anisotropic soil parameters.     

Numerical simulation of wave transformation and runup incorporating porous media wave absorber and turbulence models

A numerical wave tank is first established using the Navier–Stokes equations and the VOF method assuming laminar flow. The standard k–ε, realizable k–ε and RNG k–ε turbulent models are then incorporated to the numerical tank. An effective numerical method for wave absorption utilizing the energy-dissipating property of porous media is also included. To validate the accuracy of the proposed models, the propagation of a solitary wave, where analytical solution is available for comparison, is first simulated. This is followed by the simulation of irregular wave runup on a composite seawall, wave propagation over submerged bars and wave refraction and diffraction over an elliptic shoal, where experimental data are available for comparison. All computed results agree well with either the analytical solution or the experimental data.     

Incompressible SPH flow model for wave interactions with porous media

The paper presents an Incompressible Smoothed Particle Hydrodynamics (ISPH) method to simulate wave interactions with a porous medium. The SPH method is a mesh free particle modeling approach that is capable of tracking the large deformation of free surfaces in an easy and accurate manner. The ISPH method employs a strict incompressible hydrodynamic formulation to solve the fluid pressure and the numerical solution is obtained by using a two-step semi-implicit scheme. The ISPH flow model solves the unsteady 2D Navier–Stokes (NS) equations for the flows outside the porous media and the NS type model equations for the flows inside the porous media. The presence of porous media is considered by including additional friction forces into the equations. The developed ISPH model is first validated by the solitary and regular waves damping over a porous bed and the solitary wave interacting with a submerged porous breakwater. The convergence of the method and the sensitivity of relevant model parameters are discussed. Then the model is applied to the breaking wave interacting with a breakwater covered with a layer of porous materials. The computational results demonstrate that the ISPH flow model could provide a promising simulation tool in coastal hydrodynamic applications.     

Three-dimensional dynamic response of multilayered poroelastic media

ABSTRACT

The dynamic response of a multilayered poroelastic medium under 3D time-harmonic loading is studied using an exact stiffness method. The poroelastic medium under consideration consists of N layers of different thicknesses and properties and an underlying poroelastic half-space. The exact stiffness matrices for each layer and the underlying half-space are derived explicitly using Biot’s poroelastodynamic theory and double-dimensional Fourier transforms. Selected numerical results are presented to demonstrate the influence of various parameters on dynamic response of multilayered poroelastic media under traction and fluid loading. The application of proposed solution scheme to soil–structure interaction problems is also presented.     

Two phase modal analysis of nonlinear sloshing in a rectangular container

Sloshing, or liquid free surface oscillation, in containers has many important applications in a variety of engineering fields. The modal method can be used to solve linear sloshing problems and is the most efficient reduced order method that has been used during the previous decade. In the present article, the modal method is used to solve a nonlinear sloshing problem. The method is based on a potential flow solution that implements a two-phase analysis on sloshing in a rectangular container. According to this method, the solution to the mass conservation equation, with a nonpenetration condition at the tank walls, results in velocity potential expansion; this is similar to the mode shapes used in modal method. The kinematic and dynamic boundary conditions create a set of two-space-dimensional differential equations with respect to time. The numerical solution of this set of differential equations, in the time domain, predicts the time response of interfacial oscillations. Modal method solutions for the time response of container sloshing due to lateral harmonic oscillations show a good agreement with experimental and numerical results reported in the literature.     

Bragg reflection of sinusoidal waves due to trapezoidal submerged breakwaters

Numerical and laboratory experiments are performed to investigate characteristics of the Bragg reflection due to multi-arrayed trapezoidal submerged breakwaters. The numerical model is based on the Reynolds averaged Navier–Stokes equations with the VOF method and the k–ε turbulence closure model. As expected, the reflection coefficients increase as the array of submerged breakwaters increases in both laboratory measurements and numerical results. The resonant periods provide similar relative wave numbers regardless of the permeability and the number of arrays. The reflection coefficients due to porous breakwaters are smaller than those due to non-porous breakwaters. The velocity contours for two and three arrays are also described.     

Effect of pressurization positions on the consolidation of dredged slurry in air-booster vacuum preloading method

Abstract

Air booster vacuum preloading method is a useful method for strengthening dredged slurry. Though this method is improved effectively with the rapidly developed technology, the problem of inadequate reinforcement in deep layers of soil is still in existence. In view of the fact that the pressurizing system can effectively enhance the reinforcement effect. Therefore, this paper discusses the reinforcement effect of a new pressurizing system that put the booster pipeline at the bottom of soil. Meanwhile, another problem is found that the booster pipeline type was single at present, the action effect of different kind of booster pipeline is still uncertain. In this paper, laboratory experiments are performed to investigate the influence of two kinds of pressurization position and two types of booster pipeline on the treatment of five dredged slurry samples. The test results showed that though the vertical pressurizing system can be good to reinforce the middle soil layers, but the bottom pressurizing system can make the whole soil layer more homogeneous. Furthermore, the difference of the two kinds of booster pipeline on the reinforcement effect of soil is not significant. These results provide good guidance for practical application of air booster vacuum preloading in land reclamation project.     

A catalytic oxidation method for the determination of total nitrogen dissolved in seawater

A detailed examination of a high-temperature catalytic oxidation method for liquid samples in the analysis of total nitrogen dissolved in seawater is reported. The nitrogenous compounds in liquid samples are oxidized on a platinum catalyzer at 680°C under oxygen atmosphere and the generated NO₂ is absorbed into a chromogenic reagent, followed by a spectrophotometric determination. The results of this method are much higher than those of wet oxidation methods. Molecular size dependency of the results clearly indicates that the above discrepancy is caused by the low oxidation capacity of the wet oxidation method against high-polymer organic matter dissolved in seawater. The results revealed that the concentration of total nitrogen in seawater is nearly constant from surface to bottom, ranging from 30 to 40 μM 1^?1, which organic nitrogen concentration higher in the surface layer, and a rapid decrease with depth. An examination of molecular size distribution indicates that the concentration of high-polymer organic nitrogen decreases rapidly from surface to deeper layers, with molecular sizes ranging from 5 × 10³ to 3 × 10⁴. Because of the well-defined principle of the oxidation process, its reliability, ease of sample handling and of analytical procedure on board or in the land laboratory, the present method is much more suitable for the marine analytical chemistry of total and organic nitrogen than the other previous methods.     

Propagation of solitary waves over a submerged permeable breakwater

We study the interactions between a non-breaking solitary wave and a submerged permeable breakwater experimentally and numerically. The particle image velocimetry (PIV) technique is employed to measure instantaneous free surface displacements and velocity fields in the vicinity of a porous dike. The porous medium, consisting of uniform glass spheres, is mounted on the seafloor. Due to the limited size of each field of view (FOV) for high spatial resolution purposes, four FOVs are set in order to form a continuous flow field around the structure. Quantitative mean properties are obtained by ensemble averaging 30 repeated instantaneous measurements. The Reynolds decomposition method is then adopted to separate the velocity fluctuations for each trial to estimate the turbulent kinetic energy. In addition, a highly accurate two-dimensional model with the volume of fluid interface tracking technique is used to simulate an idealized volume-averaged porous medium. The model is based on the Volume-Averaged Reynolds Averaged Navier–Stokes equations coupled with the non-linear k–ε turbulence closure solver. Comparisons are performed between measurements and numerical results for the time histories of the free surface elevation recorded by wave gauges and the spatial distributions of free surface displacement with the corresponding velocity and turbulent kinetic energy around the permeable object imaged by the PIV system. Fairly good agreements are obtained. It is found that the measured and modeled turbulent intensities on the weather side are much larger than those on the lee side of the object, and that the magnitude of the turbulent intensity increases with increasing wave height of a solitary wave at a constant water depth. The verified numerical model is then used to estimate the energy reflection, transmission and dissipation using the energy integral method by varying the aspect ratio and the grain size of the permeable obstacle.     

波浪与多孔介质结构相互作用SPH模拟

应用经CSPM法和黎曼解修正后的光滑粒子流体动力学(SPH)方法,建立了主动吸收无反射数值波浪水槽,研究波浪作用下多孔介质结构的水动力特性。流体运动控制方程采用N-S方程,多孔渗水结构内流体的运动控制方程考虑渗流力的影响。数值计算结果给出了水槽内不同位置测点的波面历时曲线和越浪量随时间变化曲线,并同试验结果和Philip Liu的数值计算结果进行了比较。并对一个波浪周期内斜坡堤多孔介质结构内外的速度场和压力分布进行了讨论分析。计算分析表明,数值计算波面较Philip Liu的计算结果与试验结果吻合更好。说明应用SPH方法建立的二维数学模型能够较好地模拟破碎波在多孔渗水斜坡上的爬坡和越浪。